Hydrostatic drives of this type, as are shown, for example, in document WO 2007/079935 A1, are often used in commercial vehicles like buses or mobile machinery. These drive systems offer the possibility of storing a part of the kinetic energy as pressure energy during braking processes and then recovering it to support acceleration processes. In this respect, the prior art provides for at least one drive unit to be set up as a hydraulic motor in the form of an adjustable motor-pump unit so that the hydraulic motor delivers hydraulic fluid in the overrun mode of the drive system. The delivery volume is supplied as a charging volume to the high pressure accumulator, with both a braking action in the drive unit and storage of pressure energy occurring in the high pressure accumulator. This energy can be recovered by the high pressure accumulator being connected to the working line assigned to the delivery side in the drive state for acceleration processes. In the respective working cycle for acceleration and braking, the second hydraulic accumulator—the low pressure accumulator—is connected to one of the working lines to equalize the volumes that have been removed or supplied to the respective other working line.